In a device of the above type known from DE-OS 43 21 003, the problem that arises on starting of the internal combustion engine, is the adjusting piston moves at a high speed into a position of maximum displacement in which its repeated abutting is accompanied by a considerable amount of noise. This is due to the fact that, when the engine has been turned off, the hydraulic medium contained in the device gradually escapes therefrom so that the adjusting piston is no longer sufficiently supported hydraulically although, as a rule, a certain residual amount of hydraulic medium is still present. Due to the torsional vibrations of the camshaft, the adjusting piston, which is now no longer hydraulically supported, is displaced into an end position on re-starting of the engine, with the already mentioned considerable noise generation. This state prevails during the period of time between the ignition of the engine and the filling of the pressure chambers, that is to say, for a few seconds after the engine has been started.